This work presents Integer Programming (IP) techniques to tackle the problem of the International Nurse Rostering Competition. Starting from a compact and monolithic formulation in which the current generation of solvers performs poorly, improved cut generation strategies and primal heuristics are proposed and evaluated. A large number of computational experiments with these techniques produced the following results: the optimality of the vast majority of instances was proved, the best known solutions were improved by up to 15% and strong dual bounds were obtained. In the spirit of reproducible science, all code was implemented using the Computational Infrastructure for Operations Research (COIN-OR).

This work addresses the unrelated parallel machine scheduling problem with sequence‐dependent setup times, in which a set of jobs must be scheduled for execution by one of the several available machines. Each job has a machine‐dependent processing time. Furthermore, given multiple jobs, there are additional setup times, which vary based on the sequence and machine employed. The objective is to minimize the schedule's completion time (makespan). The problem is NP‐hard and of significant practical relevance. The present paper investigates the performance of four different stochastic local search (SLS) methods designed for solving the particular scheduling problem: simulated annealing, iterated local search, late acceptance hill‐climbing, and step counting hill‐climbing. The analysis focuses on design questions, tuning effort, and optimization performance. Simple neighborhood structures are considered. All proposed SLS methods performed significantly better than two state‐of‐the‐art hybrid heuristics, especially for larger instances. Updated best‐known solutions were generated for 901 of the 1000 large benchmark instances considered, demonstrating that particular SLS methods are simple yet powerful alternatives to current approaches for addressing the problem. Implementations of the contributed algorithms have been made available to the research community.